On Practical Threshold Protocols and Verifiable Secret Sharing

In today’s IT world, data holds immense importance, but it also brings significant security and privacy challenges. There are few challenges to achieve the confidentiality of data. To protect data, encryption is used to keep it safe, but it can complicate data processing. To address this issue, privacy enhancing technologies, such as multi-party computation (MPC), emerge as pivotal solutions. MPC empowers parties to perform secure data computations while preserving privacy. Another challenge we face is quantum computers, which pose a threat to our current security measures. Post-quantum cryptography is the solution, but it is relatively new and less efficient compared to traditional cryptography.

The objective of this thesis is to propose efficient cryptography protocols for both classic and post-quantum settings. The contributions in this thesis address these challenges across three main sections:

- Generic MPC: This section comprises two contributions. First, it introduces a tool for generic MPC, and second, it proposes a financial application for generic MPC.

- Cryptographic Protocols: This section presents contributions related to digital signature schemes, encompassing both standard and identity based signatures, as well as verifiable secret sharing schemes.

- Non-Generic MPC: This section includes contributions related to distributed key generation algorithms and threshold signature schemes, covering both standard and identity-based threshold signatures.

In the generic MPC section, we provide a conversion algorithm as a tool for MPC, enabling the transition between conventional IEEE double precision arithmetic and secure real number arithmetic approximations within a Linear Secret Sharing Scheme-based MPC. We also demonstrate an application of MPC by using it to address the gridlock resolution issue in Real-Time Gross Settlement (RTGS) within payment systems.

In the cryptographic protocol section, the thesis presents CSI-SharK, an efficient isogeny-based signature scheme. Additionally, it develops an identity based signature scheme based on CSI-SharK. The thesis also introduces the f irst Post-Quantum secure Non-Interactive Verifiable Secret Sharing (NI-VSS) scheme with computational and communication costs of O(n) and O(nλ), respectively. Leveraging this NI-VSS, we propose highly efficient threshold protocols, including distributed key generation protocols and threshold signature schemes.

Lastly, in the non-generic MPC section, the thesis focuses on producing efficient Distributed Key Generation (DKG) protocols and subsequently threshold signatures. Our advanced isogeny-based robust threshold signature is named ThresheR SharK. During its VSS phase, we employ our proposed fast NI-VSS, which significantly enhances ThresheR SharK’s efficiency. We then leverage ThresheR SharK to introduce the first robust identity-based threshold signature scheme based on isogenies.

This thesis contributes to improving cryptographic building blocks, making them more efficient and practical. As we enter the post-quantum era, our commitment to developing secure protocols remains strong, bridging the efficiency gap in cryptographic applications. This thesis paves the way for a secure digital future.